Doctors' leaders today urged David Cameron to "be courageous" and take a "once-in-a-lifetime opportunity to save lives".
A consultation document last year floated a base price of 45p per alcohol unit in England and Wales and the Government has yet to release its conclusions.
But a move which could see the plans being dropped is in stark contrast to the picture north of the border.
In Scotland, MSPs voted last year to approve a Bill which will introduce a minimum price for alcohol.
The Scottish Government revealed the 50p minimum unit price should be introduced this year.
However, in January, the Scotch Whisky Association brought legal action against the legislation which would introduce a minimum unit price.
According to the SWA, which represents whisky firms in Scotland, the measure is illegal and will damage the industry.
Mr Cameron had thrown his weight behind the pricing policy down south but a number of Cabinet ministers, including Home Secretary Theresa May, have made clear they harbour doubts.
Speculation has been growing for some weeks that the proposals will be shelved amid criticism that it will unfairly punish responsible drinkers on low incomes.
Dr Vivienne Nathanson, director of professional activities at the BMA, said the impact on them would be a "tiny amount" of 30p-40p per week that would be outweighed by the benefits.
She said: "Be courageous: this is a once-in-a-lifetime opportunity to save lives, to save the country money."
But senior Tory David Davis said he would welcome the abandonment of the plan.
In a swipe at the Prime Minister, he said it was "not going to change the price of Chateau Lafite at Chequers" and he dismissed the support of medics.
The former shadow home secretary said: "It will hit poor people, it will hit people in the north, it will hit the pensioner having their one bottle of wine a week.
"It will transfer £1 billion from the public to the people who sell alcohol and it's not going to work."